材料科学中神经网络性能随数据量增长不规律，但随模型参数增长有明确规律。
Broken neural scaling laws in materials science
- 用高通量计算数据训练图神经网络预测金属介电函数。
- 数据量增加时模型性能不再提升，出现失效的缩放规律。
- 适合关注机器学习在稀缺数据场景下应用的研究者。
在材料科学中，数据稀少且生成成本高昂，无论是计算还是实验。因此，识别模型性能如何随数据集规模和模型容量变化，以区分数据受限与模型受限的阶段至关重要。神经缩放定律为此提供了量化框架，指导材料数据集和机器学习架构的设计。本文研究了典型材料科学任务——预测金属介电函数（一种高维响应，决定固体与光的相互作用）的神经缩放规律。基于超过20万条来自高通量第一性原理计算的介电函数数据，我们训练了两种多目标图神经网络，用于预测频率依赖的复数间带介电函数和德鲁德频率。结果发现，随着数据集规模增大，神经缩放定律出现断裂；而随着模型参数数量增加，缩放关系遵循简单幂律并迅速饱和。
原文摘要 · Abstract (English)
In materials science, data are scarce and expensive to generate, whether computationally or experimentally. Therefore, it is crucial to identify how model performance scales with dataset size and model capacity to distinguish between data- and model-limited regimes. Neural scaling laws provide a framework for quantifying this behavior and guide the design of materials datasets and machine learning architectures. Here, we investigate neural scaling laws for a paradigmatic materials science task: predicting the dielectric function of metals, a high-dimensional response that governs how solids interact with light. Using over 200,000 dielectric functions from high-throughput ab initio calculations, we study two multi-objective graph neural networks trained to predict the frequency-dependent complex interband dielectric function and the Drude frequency. We observe broken neural scaling laws with respect to dataset size, whereas scaling with the number of model parameters follows a simple power law that rapidly saturates.
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